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arXiv:2508.10442 · Optik

High-dimensional autocompensating discrete modulation CV-QKD protocol in optical fibers

Alexandre Vázquez-Martínez, Xesús Prieto-Blanco, Eduardo F. Mateo, Jesús Liñares

Published Jul 20, 2026• 0 citations
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Abstract

In this work we present a high-dimensional discrete modulated CV-QKD protocol, with dimension , in optical fibers, where is the number of optical modes. We use -dimensional product states of weak coherent states that undergo perturbations along optical fibers and that are cancelled in a passive way (autocompensation) and then measured by a standard balanced homodyne detection. We analyze the security of this high-dimensional protocol under two types of attack. First, an intercept and resend attack implemented with simultaneous homodyne measurement in both quadratures. Then, a beam-splitter attack with channel substitution is also considered. Finally, the resulting secure key rates are calculated showing a significative increase with dimension.

DOI
10.1016/j.ijleo.2026.172837

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In this work we present a high-dimensional discrete modulated CV-QKD protocol, with dimension , in optical fibers, where is the number of optical modes. We use -dimensional product states of weak coherent states that undergo perturbations along optical fibers and that are cancelled in a passive way (autocompensation) and then measured by a standard balanced homodyne detection. We analyze the security of this high-dimensional protocol under two types of attack. First, an intercept and resend attack implemented with simultaneous homodyne measurement in both quadratures. Then, a beam-splitter attack with channel substitution is also considered. Finally, the resulting secure key rates are calculated showing a significative increase with dimension.
We present a high-dimensional quantum key distribution protocol by using N-qudits quantum light states, that is, product states with N photons, each of them in a quantum superposition of dimension d which provides a high dimension dN and accordingly a very high security. We present the implementation of this protocol in different types of optical fibers where the mentioned states undergo perturbations under propagation in optical fibers; such perturbations can be notably reduced in a passive (autocompensation) or active way and importantly the N-qubits present a great robustness against such optical perturbations. Likewise, quantum states also undergo attenuation, that is, some photons are lost under propagation in the optical fibers and then effective N′ (< N)-qudits are obtained which also are used to generate secret keys. In fact, the detection of states combines standard projective measurements along with photon coincidences. Besides, we analyze the security of this high-dimensional protocol under an intercept and resend attack realized by Eve, and the resulting secure key rates are calculated showing a significative increasing with the dimension provided by the number N of photons.
Discretely modulated continuous-variables quantum key distribution (CV-QKD) protocols are usually proposed with phase modulated coherent states being sent by Alice and simple homodyne detection on the Bob side and, in the majority of the studies, their security is analyzed assuming that for low photon number the protocols are similar to a Gaussian modulated CV-QKD. Here we discuss other detection techniques such as double homodyne, consider classical attacks and find practical strategies for the legitimate parties to reach the security limits predicted by the Gaussian modulated CV-QKD.
Abstract Continuous-variable quantum key distribution (CV-QKD) has many practical advantages including compatibility with current optical communication technology. Implementation using heterodyne measurements is particularly attractive since it eliminates the need for active phase locking of the remote pair of local oscillators, but the full security of CV QKD with discrete modulation was only proved for a protocol using homodyne measurements. Here we propose an all-heterodyne CV-QKD protocol with binary modulation and prove its security against general attacks in the finite-key regime. Although replacing a homodyne measurement with a heterodyne measurement would be naively expected to incur a 3-dB penalty in the rate-distance curve, our proof achieves a key rate with only a 1-dB penalty.
We have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.
We experimentally demonstrated an all-fiber-based unidimensional continuous-variable quantum key distribution (CV QKD) protocol and analyzed its security under collective attack in realistic conditions. A pulsed balanced homodyne detector, which could not be accessed by eavesdroppers, with phase-insensitive efficiency and electronic noise, was considered. Furthermore, a modulation method and an improved relative phase-locking technique with one amplitude modulator and one phase modulator were designed. The relative phase could be locked precisely with a standard deviation of 0.5\ifmmode^\circ\else\textdegree\fi{} and a mean of almost zero. Secret key bit rates of 5.4 kbps and 700 bps were achieved for transmission fiber lengths of 30 and 50 km, respectively. The protocol, which simplified the CV QKD system and reduced the cost, displayed a performance comparable to that of a symmetrical counterpart under realistic conditions. It is expected that the developed protocol can facilitate the practical application of the CV QKD.
Continuous-variable quantum key distribution (CV-QKD) with discrete modulation has received widespread attentions because of its experimental simplicity, lower-cost implementation and ease to multiplex with classical optical communication. Recently, some inspiring numerical methods have been applied to analyse the security of discrete-modulated CV-QKD against collective attacks, which promises to obtain considerable key rate over one hundred kilometers of fiber distance. However, numerical methods require up to ten minutes to calculate a secure key rate one time using a high-performance personal computer, which means that extracting the real-time secure key rate is impossible for discrete-modulated CV-QKD system. Here, we present a neural network model to quickly predict the secure key rate of homodyne detection discrete-modulated CV-QKD with good accuracy based on experimental parameters and experimental results. With the excess noise of about 0.010.010.01, the speed of our method is improved by about seven orders of magnitude compared to that of the conventional numerical method. Our method can be extended to quickly solve complex security key rate calculation of a variety of other unstructured quantum key distribution protocols.